Answer:
Option B. The phrase "when the great world for the first time puts out a hand to her" is an example of personification.
Explanation:
Personification is a figure of speech in which an object or a non human things or organism is given human attributes. The phrase "when the great world for the first time puts out a hand to her" is a personification as it is giving the world, which is a planet, a human attribution of "holding a hand to someone" in an effort of helping them.